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Why is the bokeh shaped like the aperture? What is the physical explanation to this?

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Simple version, because the aperture blocks out any rays of light that would have corresponded to that point that don't pass through it. Each point of light is actually the same shape as the aperture as some of the light coming from all of the aperture goes in to producing it, the only difference is that when properly focused, it all appears to be one point. When out of focus, the light spreads out some and so you see the shape of the opening that let the light in more clearly.

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Light propagates in a line, unless you make your photo near a black hole or a giant sun. Consequently, as soon as the light converges into the focal point and arrive at your sensor, you have similar cones from the aperture to the focal point and from the focal point to the sensor.

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The upper circle is in the shape of your aperture, the bottom circle is the corresponding image spot (some nearby pixels). They are of same shape.

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